A non-geometric Brownian motion model estimated by Markov chain approximation

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dc.contributor Mai, Tsun-Zee
dc.contributor Lee, Junsoo
dc.contributor Trent, Tavan T.
dc.contributor Hsia, Wei-Shen
dc.contributor.advisor Wang, Pu
dc.contributor.author Chang, Hung Yu
dc.date.accessioned 2017-03-01T16:23:55Z
dc.date.available 2017-03-01T16:23:55Z
dc.date.issued 2011
dc.identifier.other u0015_0000001_0000774
dc.identifier.other Chang_alatus_0004D_10899
dc.identifier.uri https://ir.ua.edu/handle/123456789/1278
dc.description Electronic Thesis or Dissertation
dc.description.abstract The pricing of most contingent claims is continuously monitored the movement of the underlying assets that follow geometric Brownian motion. However, for exotic options, the pricing of the underlying assets is difficult to be obtained analytically. In reality, numerical methods are employed to monitor discretized path-dependent options since complexity of exotic options increases the difficulty of obtaining the closed-form solutions. In this dissertation, we propose a Markov chain method to discretely monitor the underlying asset pricing of an European knock-out call option with time-varying barriers. Markov chain method provides some advantages in computation since the discretized time step can be partitioned to match with the number of the underlying non-dividend paying asset prices. Compared to Monte Carlo simulation, Markov chain method can not only efficiently handle the case where the initial asset price is close to a barrier level but also effectively improve the accuracy of obtaining the price of a barrier option. We study an European knock-out call option with either constant or time-varying barriers. Under risk-neural measure, the movement of the underlying stock price is said to follow a non-geometric Brownian motion. Furthermore, we are interested to estimate the parameter p value that generates optimal payoff of a knock-out option with time-varying barriers. However, implied volatility is an essential factor that affects the movement of the underlying asset price and determines whether the barrier option is knocked out or not during the lifetime of the option.
dc.format.extent 110 p.
dc.format.medium electronic
dc.format.mimetype application/pdf
dc.language English
dc.language.iso en_US
dc.publisher University of Alabama Libraries
dc.relation.ispartof The University of Alabama Electronic Theses and Dissertations
dc.relation.ispartof The University of Alabama Libraries Digital Collections
dc.relation.hasversion born digital
dc.rights All rights reserved by the author unless otherwise indicated.
dc.subject.other Mathematics
dc.subject.other Finance
dc.subject.other Engineering
dc.title A non-geometric Brownian motion model estimated by Markov chain approximation
dc.type thesis
dc.type text
etdms.degree.department University of Alabama. Dept. of Mathematics
etdms.degree.discipline Mathematics
etdms.degree.grantor The University of Alabama
etdms.degree.level doctoral
etdms.degree.name Ph.D.

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